A Normal Sequence Compressed by PPM* But Not by Lempel-Ziv 78

In this paper we compare the difference in performance of two Prediction by Partial Matching (PPM) family compressors (PPM$^*$ and original Bounded PPM algorithm) Lempel-Ziv 78 (LZ) algorithm. We construct an infinite binary sequence whose worst-case compression ratio for PPM$^*$ is $0$, while PPM's LZ's best-case ratios are at least $1/2$ $1$ respectively. This enumeration all strings order length, i.e. length followed $2$ so on. It therefore normal, built using repetitions de Bruijn increasing